cartan-dec

Discrete exterior calculus on Riemannian manifolds.

Part of the cartan workspace.

Overview

cartan-dec bridges continuous Riemannian geometry (cartan-core) to discrete differential operators for PDE solvers on simplicial meshes. All metric information flows through the Hodge star; topology is encoded in the metric-free exterior derivative.

The crate provides:

• Mesh<M, K, B>, a generic simplicial complex parameterized by manifold type M, simplex dimension K, and embedding dimension B.
• ExteriorDerivative, sparse boundary operators d0 and d1 (via sprs).
• HodgeStar, diagonal Hodge star operators indexed by form degree.
• Operators, assembled Laplace-Beltrami, Bochner, and Lichnerowicz Laplacians.
• Upwind covariant advection and discrete divergence for scalar, vector, and tensor fields.

All operators are generic over M: Manifold with const generics K and B, so the same code works on flat meshes and curved Riemannian surfaces.

Example

use cartan_dec::{FlatMesh, Operators};
use cartan_manifolds::Euclidean;
use nalgebra::DVector;

// Build a 4x4 uniform triangular grid on [0,1]^2.
let mesh = FlatMesh::unit_square_grid(4);
let ops = Operators::from_mesh(&mesh, &Euclidean::<2>);

// Apply the scalar Laplacian to a vertex field.
let f = DVector::from_element(mesh.n_vertices(), 1.0);
let lf = ops.apply_laplace_beltrami(&f);

License

MIT